Does Blender have Smooth Mesh Preview?
No,as far as I know Blender does not have smooth mesh preview. When I change from Maya to Blender it bothered me as well but soon you will get use to it and you realize you dont need it.

Instead of it you can use subdivision surface modifier and its options to turn it on/off in different modes. It is convenient to let it smooth the object in view port but turn it of when you are in the edit mode.

Shade smooth is kind of the same as smooth normals in Maya